The imposition of the curfew had been announced a few hours earlier by the mayor and NY state governor Andrew Cuomo after protests and looting during the weekend - notably in the trendy SoHo district.
They also urged protesters to cover their faces as the city remains the epicenter of the COVID-19 pandemic.
Groups of young people moved from block to block around the district, usually bustling with tourists but deserted due to the coronavirus, with entire streets blocked by police. Wreckage littered the inside of an AT&T store.
Freddi Goldstein, a spokesman for de Blasio, called Cuomo's remarks "offensive to the men and women of the NYPD, who are out there every night trying to keep New Yorkers safe".
Twitter temporarily suspended the account of a major New York City police union on Monday for posting the arrest report of New York Mayor Bill de Blasio's daughter, including her personal information.
"We can't let violence undermine the message of this moment", de Blasio said in a written statement. Another trooper and a Buffalo police officer were treated for minor injuries after being struck by the Ford Explorer after it broke through a blockade at about 10 p.m. Monday.
Big crowds rallied in Times Square and Brooklyn in the afternoon and then problems started in the evening.
Joe Biden to deliver address from Philadelphia amid nationwide unrest
Protests have intensified in recent days, particularly in Washington, D.C. Trump made no attempt to link Floyd's death to any broader question.
SpaceX Crew Dragon docks with International Space Station
The spaceship's hatch opened at 1:02 pm Eastern Time (1702 GMT) as Bob Behnken and Doug Hurley carried out final procedures before crossing the threshold about 20 minutes later.
Pubs to re-open in the UK Boris says
He defended Mr Cummings' actions and said people could "exercise a degree of personal judgment" in following lockdown laws. Dominic Cummings drove over 400km with his wife, who had Covid-19 symptoms, so family could care for their son.
De Blasio noted that daytime demonstrations over the last five days have been overwhelmingly peaceful.
The deliberations came as workers swept up broken glass outside luxury stores in Manhattan's chic SoHo neighbourhood, where people smashed windows and plundered shops overnight.
Earlier in the day, one Times Square demonstrator, Giselle Francisco, considered the curfew necessary.
"But as the night wears on we are seeing groups use them to incite violence and destroy property", the mayor said. "What happened in New York City was inexcusable", Cuomo said. "There were thousands of people in that area at that time". Hundreds were arrested, Shea said.
Earlier on Monday, de Blasio said at his daily briefing that he is planning to talk with other officials on a potential curfew in the nation's largest city.
"There are people using this as a reason to create chaos and be violent", she added. She was cited with a desk appearance ticket, which is handed out instead of a custodial arrest.
Her father said Monday she told him she'd behaved peacefully and believed she had followed police officers' instructions.
De Blasio has generally been supportive of the police response to protesters in recent days, even when pressed by reporters on aggressive law enforcement methods documented across the city.